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When held by Dialga, the Adamant Orb multiplies the power of all damage-dealing Dragon- and Steel-type moves used by the holder by 4915/4096 (approximately 1.2). Can be held by other Pokemon, but then has no effect.
Since Adamant Orb only has an effect when held by Dialga, naturally the only time you would want to use it would be with a Dialga, but even then it is essentially useless in competitive play as Life Orb is just better for pretty much anything Dialga can do, providing a 30% boost to all of Dialga's moves, as opposed to 4915/4096 just to Dragon- and Steel-type moves. It can potentially be useful for bluffing a Choice item, but Expert Belt is normally a better choice for that strategy, as it is not limited to Dialga's STAB attacks.
Marvelous Bridge (given by the Shadow Triad).